Further, sources "at the top of the Trump transition team" confirmed to New York Times political reporter Jeremy Peters that she "went rogue" at Trump's expense, "Morning Joe" reported.

"Kellyanne went rogue at Donald Trump's expense at the worst possible time, a source familiar with Trump's thinking said," Peters reported. A top Trump aide was "baffled" by Conway's comments. The source suggested it feeds into a growing concern inside the campaign that "instead of driving Donald Trump's message she's pushing her own agenda."

Another top transition aide called her comments "dangerous," said Peters. "Steve Bannon and Reince Priebus have reportedly been growing frustrated by Kellyanne Conway's failure to become a team player in a transition process where the top players are forming a tight knit group around the president-elect."

Conway texted the show to complain that the coverage of her comments was "sexist" and that Trump "wants me by his side."

"[She said] she can have any job she wants," said host Joe Scarborough, who first reported that Trump was "furious."

"I'm not sure how that reporting is sexist because those were sources at the top of the campaign," Scarborough added. "Is she suggesting that people inside the campaign ... Donald Trump, according to people at the top of the campaign closest to Donald Trump, are saying he was furious and certainly he would not approve somebody saying that they betrayed their supporters. Is this sexist?"

On Sunday, Conway, told CNN's "State of the Union" that it is not known "if Mitt Romney voted for Donald Trump," and that she's "all for party unity, but I'm not sure we have to pay for that with the secretary of state position."

Conway, Peters reported, suggests that Romney would preside over something of a "rogue agency" — a feeling shared by others in the Trump camp.

"What they're worried about is that Mitt Romney and his allies, if installed in the State Department, would operate completely independently from the White House and any time there was any kind of distance between the White House and the State Department that there would be efforts to make the State Department look better vis-a-vis the White House," said Peters.

Scarborough ridiculed the idea that Conway would try to "box him [Trump] in by calling him a betrayer."

Former New York City Mayor Rudy Giuliani "is not going to box him in," said Scarborough. "It's going to make him look weak if he goes with Giuliani now... suggesting that Donald Trump is going to let any agency go rogue is such an insult to Donald Trump, it's staggering. That Donald Trump is going to be weak and Mitt Romney said something, that would be bad. No. He would fire him that day."

Scarborough continued that Conway made her comments because she does not have a job in the Trump administration and "she's angry about that."

"She hasn't been offered the job she wants, she is [angry], I can report that, and so she's striking out," said Scarborough. "She's not in meetings where these decisions are being made and she's angry about that. At the same time, you don't go out and attack the vice president-elect because you're mad at Reince Priebus."

"Romney is not dead for this job because there are very senior people in the transition who are strategizing about how to make this happen still," he said. "But this issue of an apology is front and center. I don't think Romney is going to want to apologize the way some Trump supporters are saying are the price for being considered."

Romney not only won't apologize, but Trump doesn't want him to, said Scarborough.

"What Donald Trump told me is when the first came up, he was tough on you," said Scarborough. "Donald Trump said I beat him up for five years. I was rough on him too. I like the fact that the guy pushes back."

Political commentator Mike Barnicle agreed that his sources close to Romney have said he won't apologize for his tough words against Trump during the 2016 election season.

"I can also report that the problem wouldn't be a rogue Secretary of State," said Barnicle. "The bureaucracy within the State Department is of its own weight something that's very difficult to move. There's one way to clear this up for Donald Trump to appoint secretary of state today.

Scarborough said his sources are telling him that Conway "went completely rogue" with her statements and that they did not come from the campaign.

"Donald Trump was furious yesterday that she would take that upon herself to keep attacking Mitt Romney," said Scarborough.